Welcome Email Going to Spam

Add SPF record to your DNS so emails from your server IP are classified as legitimate

Edit.
Do the above with what you said.
“Would setting up a domain specific email address and changing the site owner email to ***@thedomain.com help keep these messages from going into spam folders?”

This will be fine as it will be the smtp server on your Web server which is sending the emails and hence will now get through spam checks